Method for designing sector beam antennas

ABSTRACT

An improved method for designing sector beam antennas. The method is used to provide a sector beam antenna having a feed horn with a cross sectional azimuth dimension and a cross sectional elevational dimension which are optimized to irradiate a reflector to transmit a signal over a coverage area such that the gain-area-product of the transmitted signal is maximized.

REFERENCE TO PARENT APPLICATION

This is a continuation-in-part of application Ser. No. 06/672,739 forHigh Gain Area Product Antenna Design, filed Nov. 19, 1984 by James D.Thompson and Gregory S. Czuba, now abandoned.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to sector beam antennas. Moreparticularly, the present invention relates to a method for designing asector beam antenna with a high gain-area-product (GAP).

While the invention is described herein with respect to a particularimplementation with reference to an illustrative embodiment, it isunderstood that the invention is not limited thereto. Those of ordinaryskill in the art will recognize additional applications of the teachingsprovided herein within the scope of the present invention.

2. Description of the Related Art

Where it is necessary to provide area coverage by an antenn, i.e., forcommunication satellites, it is often desirable to provide the highestpossible gain with uniform coverage. In a communication satellite, forexample, it may be desirable to provide uniform coverage within adesignated area such as the continental United States. Area coverage iscurrently accomplished using antennas constructed in accordance withconventional design techniques. In some cases, several antennas are usedto provide overlapping sector beams. This approach may be somewhatelaborate and require the coordination of a cluster of multiplegeosynchronous satellites, i.e., one for each section of the regionalarea of coverage. See U.S. Pat. No. 4,375,697 to Visher.

Another common solution is to provide a single antenna system with amultiple feed array shaped roughly in proportion to the region intendedto be covered. The electromagnetic signal energy is apportioned amongthe feed elements. The reflector projects a set of overlapping beams inorder to attempt to achieve full coverage of the regional area withapproximately the same gain factor over the entire area. These systemsare typically complex, using computerized assistance to select theoptimum arrangement of amplitudes and phases needed to coordinate theexcitations. Also, such systems often have high power requirements whichmay be difficult to achieve in a particular application.

Although it is well known that a useful figure of merit for sector beamantennas is the gain-area-product (GAP), conventional sector beamantennas are designed to maximize the peak gain. (The GAP is the productof the minimum gain of the antenna, in the coverage area, and theangular coverage area of the coverage region.) The Antenna EngineeringHandbook by H. Jasik 1961 (page 2-14) gives a relationship between gainand beamwidth which results in a theoretical GAP value of 10,600 deg²for antennas of traditional design. This agrees with current antennapractice, which achieves coverage beams with GAP values ranging from10,000 to 15,000 deg². For a theoretically ideal sector beam withuniform gain within the coverage region and with no gain outside thecoverage region, the GAP is 41,253 deg². Thus, current practice producesantenna beams with GAP values of 25% to 35% of the maximum achievablegain-area-product.

SUMMARY OF THE INVENTION

The shortcoming illustrated by the related art are addressed by thepresent invention which provides an improved method for designing asector beam antenna to maximize the gain-area-product thereof. Themethod is used to provide a sector beam antenna having a feed horn witha cross sectional azimuth dimension d_(A) and a cross sectionalelevational dimension d_(E) which are optimized to irradiate a reflectorhaving a cross sectional diameter D, so as to transmit a signal having afundamental frequency f of wavelength L over a coverage area A such thatthe gain-area-product thereof is maximized. The azimuth beamwidth forthe coverage area is B_(A) and the desired elevation beamwidth for thecoverage area is B_(E). The method of the invention includes the stepsof:

(a) dividing the reflector diameter D by the wavelength L to obtain aratio D/L;

(b) multiplying the azimuth beamwidth B_(A) by the ratio D/L to obtain afirst product equal to B_(A) D/L;

(c) multiplying the elevation beamwidth B_(E) by the ratio D/L to obtaina second product equal to B_(E) D/L;

(d) ascertaining the value of a first index K_(A) from said firstproduct, which is proportional to the primary energy distribution of thefeed horn in azimuth and provides a measure of the extent to whichsidelobes of the signal, radiated in azimuth as part of the primarypattern from the feed horn, irradiate the reflector as a function of anangle O_(A) between a first line from the center of the feed horn to thecenter of the reflector and a second line from the center of the feedhorn to the edge of the reflector in the azimuth direction;

(e) ascertaining the value of a second index K_(E) from said secondproduct, which is proportional to the primary energy distribution of thefeed horn in elevation and provides a measure of the extent to whichsidelobes of the signal, radiated in elevation as part of the primarypattern from the feed horn, irradiate the reflector as a function of asecond angle O_(E) between the line from the center of the feed horn tothe center of the reflector and a third line from the center of the feedhorn to an edge of the reflector in the elevation direction;

(f) determining the azimuth dimension d_(A) of the feed horn from thevalue of the index K_(A) which provides a first gain-line-product of thefeed horn aperture radiation pattern in azimuth; and

(g) determining the elevational dimension d_(E) of the feed horn fromthe value of the index K_(E) which provides a second gain-line-productof the feed horn aperture radiation pattern in elevation.

In a specific embodiment, the invention provides a method ofascertaining the values of the K indices which includes the steps ofcreating a graph of the K indices as a function of the BD/L productsover a range of values thereof by applying a known radiation pattern tothe reflector and measuring the width of the reflected beam. The valuesof K for a given product are then simply read from the graph.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a simplified top plan view of a conventional sector beamantenna.

FIG. 2 shows a perspective view of the conventional sector beam antennaof FIG. 1.

FIGS. 3a and 3b show an ideal distribution and corresponding idealsector beam respectively.

FIGS. 4a and 4b show a truncated distribution and corresponding sectorbeam respectively.

FIG. 5 shows the scaling factor K as a function of the beamwidthdiameter over wavelength product.

FIG. 6 shows gain-area-product as a function of the scaling parameter K.

DESCRIPTION OF THE INVENTION

FIG. 1 shows a simplified top plan view of a conventional sector beamantenna 10 having a feed horn 12 and a reflector dish 14. The feed horn12 is aligned with the reflector 14 so that energy radiated in a primaryradiation pattern therefrom will irradiate the reflector 14. That is,the boresight of the feed horn 12, emanating from the center thereof, iscoaxial with the reflector 14. (It is known that the feed horn 12 may beoff axis relative to the reflector 14. It is similarly, immaterial toconventional systems or to the present invention whether a single dishantenna such as that shown in FIG. 1 is used of an array or reflectors.)

To facilitate the description of the present invention, thecross-sectional azimuth dimension `d_(A) ` of the feed horn 12 and thecross-sectional diameter `D` of the reflector 14 are shown in FIG. 1.Also shown is the angle O_(A) between the line from the center of thefeed horn 12 and the center of the reflector 14 and a second line fromthe center of the feed horn 12 to the edge of the reflector 14. Thesector beam antenna 10 is shown in perspective in FIG. 2 where thecross-sectional elevational dimension `d_(E) ` and the elevation angleO_(E) are shown.

In general and as mentioned above, the related art teaches a design ofsector beam antennas to maximize the peak gain. The method of thepresent invention teaches a design of sector beam antennas to maximizethe gain-area-product of the reflected beam.

Thus, for an illustrative rectangular shaped beam, the design techniqueof the present invention begins with several conventional preliminarysteps including, first, selection of a reflector diameter D. Thisparameter is usually set by other, typically physical, satellite designconstraints. Next, the operating frequency f is chosen. This is oftengiven as a range with the center frequency thereof used for the designof the antenna. From the frequency f, the wavelength L is known as c/f,where c is the velocity of propagation. Since the coverage area `A` istypically given also, and the orbital distance of the satellite isknown, e.g., approximately 23,400 miles for synchronous orbit, thedesired azimuth beamwidth B_(A) and the desired elevation beamwidthB_(E) are known. For the continental United States (CONUS), for example,the azimuth beamwidth B_(A) is typically 6 degrees and the elevationbeamwidth B_(E) is typically 3 degrees.

For the illustrative rectangular shaped beam, the improved sector beamantenna design technique of the present invention includes, theadditional steps of:

(a) dividing the reflector diameter D by the wavelength L to obtain aratio D/L;

(b) multiplying the azimuth beamwidth B_(A) by the ratio D/L to obtain afirst product equal to B_(A) D/L;

(c) multiplying the elevation beamwidth B_(E) by the ratio D/L to obtaina second product equal to B_(E) D/L;

(d) ascertaining the value of a first index K_(A) from said firstproduct, which is proportional to the primary energy distribution of thefeed horn 12 in azimuth and provides a measure of the extent to whichsidelobes of the signal, radiated in azimuth as part of the primarypattern from the feed horn 12, irradiate the reflector 14, as a functionof an angle O_(A) between the first line from the center of the feedhorn 12 to the center of the reflector 14 and a second line from thecenter of the feed horn 12 to the edge of the reflector 14 in theazimuth direction;

(e) ascertaining the value of a second index K_(E) from said secondproduct, which is proportional to the primary energy distribution of thefeed horn 12 in elevation and provides a measure of the extent to whichsidelobes of the signal, radiated in elevation as part of the primarypattern from the feed horn 12, irradiate the reflector 14, as a functionof a second angle O_(E) between the line from the center of the feedhorn 12 to the center of the reflector 14 and a third line from thecenter of the feed horn to an edge of the reflector in the elevationdirection;

(f) determining the azimuth dimension d_(A) of the feed horn 12 from thevalue of the index K_(A) which provides a first gain-line-product of thefeed horn radiation pattern in azimuth; and

(g) determining the elevational dimension d_(E) of the feed horn 12 fromthe value of the index K_(E) which provides a second gain-line-productof the feed horn aperture radiation pattern in elevation.

From basic aperture theory as applied to the ideal sector beam, acircular ideal sector beam is formed when a circularly symmetricdistribution of the form 2J₁ (r)/r is put on a circular aperture ofinfinite extent. In this formulation r is the radial coordinate and J₁(r) is a Bessel function of order 1. This distribution and the resultingbeam are shown in FIGS. 3a and 3b respectively. While an infiniteaperture is not realizable in a practical sense, truncated versions ofthis same aperture distribution on a finite aperture result in beamshapes which closely approximate the ideal sector beam. A truncateddistribution and resulting beam are shown in FIGS. 4a and 4brespectively. In general, the approximation to the ideal sector beamimproves as the aperture grows radially to encompass more of thedistribution function before truncation occurs. The design technique ofthe present invention incorporates these principles which are applied,in the illustrative embodiment to a rectangular aperture 12. Thus, theindices K_(A) and K_(E) relate to the antenna parameter `mu` which is ameasure of the amount of the distribution function 2J₁ (r)/r which iscontained on the reflector 14. and is given by equation 1:

    mu=(pi)(d/L)sin 0                                          (1)

By removing the constant pi from the equation, the zero crossings of muoccur at integer multiples of d as opposed to integer multiples of pi.Thus, the parameter K, which is also a measure of distribution functioncontained on the aperture, is defined as:

    K=mu/pi=(d/L)sin 0.                                        (2)

Equation 2 may be solved for the feed horn aperture diameter d:

    d=KL/sin 0                                                 (3)

As will be evident to one of ordinary skill in the art, for a particulardistribution, where K or mu is known, the necessary aperture size d maybe determined. Where, as is typical, the aspect ratio between the focallength l and the diameter D of the reflector 14 is such that the anglesO_(A) and O_(E) are 30 degrees, d is equal to KL/2.

For the present invention, a correlation between the product of thebeamwidth B_(A) or B_(E) was determined by empirical analysis togenerate the graph of FIG. 5. FIG. 5 shows BD/L products as a functionof K for a single feed horn having a practically uniform distribution.The data for the graph was generated by applying a radiation pattern tothe reflector 14 representing a known value of K and measuring the gainand beamwidth characteristics of the resulting beam.

In operation, assume that an application requires a Ku band antenna tocover the continental United States. Assume further that a reflectorantenna is used for which a typical diameter is approximately 100inches. At Ku band, L is approximately 1 inch. As mentioned above, thebeamwidths B_(A) and B_(E) to cover CONUS are 6 degrees and 3 degreesrespectively. Accordingly, the azimuth (first) product and theelevational (second) product are respectively:

    B.sub.A D/L=6×100/1=600

and

    B.sub.E D/L=3×100/1=300.

From FIG. 5, K_(A) and K_(E) are read as 5.75 and 3.1 respectively.Using equation 3 and assuming the typical 30 degree aspect ratio,mentioned above, yields:

    d.sub.A =2.875 inches and d.sub.E =1.55 inches.

Hence the dimensions of the feed horn 12 are determined.

Moreover, with the dimensions of the feed horn 12, the performance ofthe antenna 10 may be predicted and it is substantially higher thanthose indicated above for antennas designed using the teachings of therelated art. That is, FIG. 6 shows the gain-line-product GLP versus Kfor a single feed horn having a practically uniform distribution. (Thedata of FIG. 6 was obtained by parametric study. The appropriatemathematical expressions associated with this process were obtained fromMicrowave Antenna Theory and Design by S. Silver.) Thus, GLP_(A)corresponding to a K_(A) of 5.75 is read as approximately 166 whileGLP_(E) corresponding to a K_(E) of 3.1 is similarly read as 147.Accordingly, the gain-area-product (GAP) is the product of GLP_(A) andGLP_(E) :

    GAP=(GLP.sub.A)(GLP.sub.E)=166×147=24,402 deg.sup.2.

This compares to GAP values in the range of 10,000 to 15,000 for thesector beam antennas of conventional design. In addition, given themaximum attainable GAP value of 41,253 deg² from above, the maximumattainable GLP is the square root of the maximum GAP or 203. Thus, theefficiencies in terms of GAP values for the antenna designed inaccordance with the teachings of the present invention are 166/203 or82% in azimuth and 72% in elevation.

While the present invention has been described herein with reference toan illustrative embodiment it is understood that the invention is notlimited thereto. Those of ordinary skill in the art will recognizeadditional modifications and embodiments within the scope thereof. Forexample, the invention is not limited to any particular technique forascertaining the amount of the radiated energy that irradiates thereflector as part of the primary radiation pattern. Other techniqueswithin the scope of the invention may be employed as is known in theart.

It is intended by the appended claims to cover any and allmodifications, applications and embodiments within the scope of thepresent invention. Thus,

What is claimed is:
 1. An improved method for designing a sector beamantenna to maximize the gain-area-product thereof, said sector beamantenna having a feed horn with a cross sectional azimuth dimensiond_(A) and a cross sectional elevational dimension d_(E) which irradiatesa reflector having a cross sectional diameter D, said sector beamantenna effective to transmit a signal having a fundamental frequency fof wavelength L over a coverage area A from a known distance such thatthe desired azimuth beamwidth for the coverage area is B_(A) and thedesired elevation beamwidth for the coverage area is B_(E), saidimproved method including the steps of:(a) dividing the reflectordiameter D by the wavelength L to obtain a ratio D/L; (b) multiplyingthe azimuth beamwidth B_(A) by the ratio D/L to obtain a first productequal to B_(A) D/L; (c) multiplying the elevation beamwidth B_(E) by theratio D/L to obtain a second product equal to B_(E) D/L; (d)ascertaining the value of a first index K_(A) from said first product,which is proportional to the primary energy distribution of the feedhorn in azimuth and provides a measure of the extent to which sidelobesof the signal, radiated in azimuth as part of the primary pattern fromthe feed horn, irradiate the reflector as a function of an angle O_(A)between a first line from the center of the feed horn to the center ofthe reflector and a second line from the center of the feed horn to theedge of the reflector in the azimuth direction; (e) ascertaining thevalue of a second index K_(E) from said second product, which isproportional to the primary energy distribution of the feed horn inelevation and provides a measure of the extent to which sidelobes of thesignal, radiated in elevation as part of the primary pattern from thefeed horn, irradiate the reflector as a function of a second angle O_(E)between said line from the center of the feed horn to the center of thereflector and a third line from the center of the feed horn to an edgeof the reflector in the elevation direction; (f) determining the azimuthdimension d_(A) of the feed horn from the value of the index K_(A) whichprovides a first gain-line-product of the feed horn radiation pattern inazimuth; and (g) determining the elevational dimension d_(E) of the feedhorn from the value of the index K_(E) which provides a secondgain-line-product of the feed horn aperture radiation pattern inelevation.
 2. The improved method for designing a sector beam antenna ofclaim 1 including the step of creating a graph of the index K_(A) as afunction of said first product over a range of values of said firstproduct prior to the step (d) of ascertaining the value of a first indexK_(A) from said first product.
 3. The improved method for designing asector beam antenna of claim 2 wherein said step (d) of ascertaining thevalue of a first index K_(A) from said first product includes the stepof reading the value of K_(A) from said graph corresponding to the valueof said first product.
 4. The improved method for designing a sectorbeam antenna of claim 1 including the step of creating a graph of theindex K_(E) as a function of said second product over a range of valuesof said second product prior to the step (e) of ascertaining the valueof a second index K_(E) from said second product.
 5. The improved methodfor designing a sector beam antenna of claim 4 wherein said step (e) ofascertaining the value of a second index K_(E) from said second productincludes the step of reading the value of K_(E) from said graphcorresponding to the value of said first product.
 6. An improved methodfor designing a sector beam antenna to maximize the gain-line-productthereof, said sector beam antenna having a feed horn with a crosssectional dimensional `d` and which irradiates a reflector having across sectional diameter D, said sector beam antenna effective totransmit a signal having a fundamental frequency f of wavelength L overa coverage area A from a known distance such that a desired beamwidthfor the coverage area is B, said improved method including the stepsof:(a) dividing the reflector diameter D by the wavelength L to obtain aratio D/L; (b) multiplying the beamwidth B by the ratio D/L to obtain aproduct equal to BD/L; (c) ascertaining the value of an index K fromsaid product, which is proportional to the primary energy distributionof the feed horn and provides a measure of the extent to which sidelobesof the signal radiated as part of the primary pattern from the feedhorn, irradiate the reflector as a function of the angle O between afirst line from the center of the feed horn to the center of thereflector and a second line from the center of the feed horn to an edgeof the reflector; (d) determining the dimension `d` of the feed hornfrom the value of the index K which provides a maximum gain-line-productof the feed horn aperture radiation pattern.
 7. The improved method fordesigning a sector beam antenna of claim 6 including the step ofcreating a graph of the index K as a function of said product over arange of values of said product prior to the step of ascertaining thevalue of said index K from said product.
 8. The improved method fordesigning a sector beam antenna of claim 7 wherein said step ofascertaining the value of said index K from said product includes thestep of reading the value of K from said graph corresponding to thevalue of said product.
 9. The improved method for designing a sectorbeam antenna of claim 7 wherein said step of creating a graph of theindex K as a function of said product over a range of values of saidproduct includes the step of applying a known radiation pattern to saidreflector corresponding to each value of K in a range and measuring thewidth of the reflected beam.
 10. The improved method for designing asector beam antenna of claim 6 wherein said step (d) for determining thedimension `d` of the feed horn from the value of the index K whichprovides a maximum gain-line-product of the feed horn aperture radiationpattern, includes the step of solving the equation K=d/2L for d.